DUE 6-13: Facilitators Guide Template - CC 6-12.docx

Module Focus: Statistics and Probability Grades 6-11

Sequence of Sessions

Overarching Objectives of this November 2013 Network Team Institute

Module Focus sessions for K-5 will follow the sequence of the Concept Development component of the specified modules, using this narrative as a tool for achieving deep understanding of mathematical concepts. Relevant examples of Fluency, Application, and Student Debrief will be highlighted in order to examine the ways in which these elements contribute to and enhance conceptual understanding.

High-Level Purpose of this Session

Participants will understand the coherence of the statistics work that is woven throughout the curriculum across the grade levels.

Related Learning Experiences

This session is part of a sequence of Module Focus sessions examining the Statistics and Probability curriculum, A Story of Ratios and A Story of Functions.

Key Points

Mathematical Thinking

Explain patterns

Often a deterministic way of thinking

Statistical Thinking

Search for patterns in the presence of variability

Acknowledge role of chance variation (distinguish signal from noise)

Three overarching themes of statistics and probability in Grades 6-11 include:

Variability

Learning from Data (The Investigative Process)

Probability

Session Outcomes

What do we want participants to be able to do as a result of this session?

How will we know that they are able to do this?

Focus. Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for teaching these modules.

Coherence: P-5. Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that develop within each module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the same . (Specific progression document to be determined as appropriate for each grade level and module being presented.)

Standards alignment. Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the module addresses the major work of the grade in order to fully implement the curriculum.

Implementation. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students while maintaining the balance of rigor that is built into the curriculum.

Instructional supports. Participants will be prepared to utilize models appropriately in promoting conceptual understanding throughout A Story of Units.

Participants will be able to articulate the key points listed above.

Session Overview

Section

Time

Overview

Prepared Resources

Facilitator Preparation

Statistical Thinking vs Mathematical Thinking

12 Minutes

Establish the distinction between statistical and mathematical thinking.

Statistics and Probablity in Grades 6-11 PPT

Grade 6 11 Statistics and ProbabilityOverarching Themes

23 Minutes

Explore the themes that connect statistics and probability across the grades within A Story of Ratios and A Story of Functions.

Statistics and Probablity in Grades 6-11 PPT

Linking the Two Statistics Themes

5 Minutes

Establish that the theme of learning from data through the investigative process is inherently tied to the theme of variability

Statistics and Probablity in Grades 6-11 PPT

Example Trajectory

26 Minutes

Provide examples from the lessons of grades 6, 7 and 11 that show how students develop and mature in their understanding over one of the overarching themes.

Statistics and Probablity in Grades 6-11 PPT

Other Developmental Dimensions

29 Minutes

Describe other developmental trajectories in the statistics content in order to show how students are expected to develop deeper understanding as they move from grade 6 to grade 11.

Statistics and Probablity in Grades 6-11 PPT

Questions and Discussion

0 Minutes

Answer questions and facilitate discussion.

Session Roadmap

Section: Statistical Thinking vs Mathematical Thinking

Time: 12 minutes

[12 minutes] In this section, you will

Distinguish between mathematical and statistical thinking

Materials used include:

Time

Slide #

Slide #/ Pic of Slide

Script/ Activity directions

GROUP

1

1

NOTE THAT THIS SESSION IS DESIGNED TO BE 90 MINUTES IN LENGTH.

Welcome! In this session, we will examine the study of statistics and probability across grades 6-11 in A Story of Ratios and A Story of Functions.

1

2

Introduce the objectives for this session:

Distinguish between mathematical and statistical thinking

See how statistical thinking is developed in the statistics content of Grades 6 11

Because the statistics content is spread over multiple grades, it is important for teachers to understand the overarching themes that provide coherence to the statistics curriculum.

Examples from the lessons will be used to illustrate conceptual development across grades.

1

3

Go over the agenda for the session. The session is divided into 5 parts, followed by time for questions and discussion. Advise participants that even though there will be time for questions at the end, they can ask questions as you go through the presentation. There will be several activities and participants are encouraged to participate in those activities. The activities are based on classroom activities from the lessons, but have been modified in anticipation of a group much larger than a typical class.

1

4

Introduce the scenario described on this slide. Ask for thoughts on what is happening here. Most math folks will see a pattern here and attempt to come up with explanations for why the pattern exists. For example, often people suggest that it is a contagious disease that started in the county in the lower right. Others might say it is a mosquito borne disease and there is a big area of stagnant water in the lower right county. People come up with all kinds of creative explanations.

However, almost never does anyone suggest that this might just be something that occurs at random and that the numbers observed in the different counties are just consistent with chance differences that would be expected as consistent with random behavior. This is the big point. IN fact, these numbers are just random digits.

The statistical thinker would know to ask the questioncould this just have happened by chance? Only if chance could be ruled out as a plausible explanation for the pattern should we be convinced that some else is at work here and go looking for other explanations.

1

5

Summarize this slide, referring back to the discussion from the previous slide. Emphasize that statistical thinking is not a deterministic way of thinking. Looks for pattern in the presence of variability, recognizes the role of chance.

8

6

The main point here is that statistical thinking is complex. It is a different way of thinking. Both mathematical and statistical thinking are important. Mathematical thinking is developed slowly over 12 years of school. Likewise, statistical thinking needs to be developed and nurtured. It is not something that kids will just get with a quick or superficial exposure.

Section: Grade 6 11 Statistics and ProbabilityOverarching Themes

Time: 23 Minutes

[23 minutes] In this section, you will

Explore the themes that connect statistics and probability across the grades within A Story of Ratios and A Story of Functions

Materials used include:

Time

Slide #

Slide #/ Pic of Slide

Script/ Activity directions

GROUP

1

7

This slide just transitions to the next section: The placement of statistics and probability in the grade 6 1 curriculum and overarching themes that provide coherence.

2

8

This curriculum overview chart shows the placement of the statistics and probability content in Grades 6 8.

1

9

This curriculum overview chart shows the placement of the statistics and probability content in Grades 9 - 11. Notice that there is no statistics component in Grade 10.

1

10

The way that statistics is placed in the common core presents some challenges that teachers should be aware of. Because it is spread over any grade levels, it is easy for it to be seen as bits and pieces in isolation. Without a big picture of how it all fits together, it might be perceived as just an odd collection of tools. We want to avoid a curriculum that is perceived as Another year, another graph

A second challenge is that there are long time gaps between statistics modulesin some cases more than 2 years (between grade 9 module 2 and grade 11 module 4). There are some connections that need to be made from grade 7 in grade 11! Teachers may find it necessary to do some reviewing of concepts, which may require teachers to be familiar with the statistics content from grade levels other than the one they regularly teach.

The final challenge is that the statistics content in the common core is content that most teachers have not had to teach prior to the common core. Many secondary teachers and almost all middle s